Observe the following equations:
$Ag^{+} + NH_3 \rightleftharpoons [Ag(NH_3)]^{+}$,$K_1 = 1.6 \times 10^3$
$[Ag(NH_3)]^{+} + NH_3 \rightleftharpoons [Ag(NH_3)_2]^{+}$,$K_2 = 6.8 \times 10^3$
The equilibrium constant for the following reaction,$Ag^{+} + 2 NH_3 \rightleftharpoons [Ag(NH_3)_2]^{+}$ is

$A$ vessel at $1000 \ K$ contains $CO_2$ with a pressure of $0.5 \ atm$. Some of $CO_2$ is converted into $CO$ on addition of graphite. If total pressure at equilibrium is $0.8 \ atm$,then $K_P$ is : (in $atm$)

The equilibrium composition for the reaction $PCl_3 + Cl_2 \rightleftharpoons PCl_5$ at $298 \, K$ is given below.
$[PCl_3]_{eq} = 0.2 \, mol \, L^{-1}$
$[Cl_2]_{eq} = 0.1 \, mol \, L^{-1}$
$[PCl_5]_{eq} = 0.40 \, mol \, L^{-1}$
If $0.2 \, mol$ of $Cl_2$ is added at the same temperature,the equilibrium concentration of $PCl_5$ is $.... \times 10^{-2} \, mol \, L^{-1}$. Given: $K_c$ for the reaction at $298 \, K$ is $20$.

For the reaction $N_2 + O_2 \rightleftharpoons 2NO$ at $300 \, ^\circ C$,the value of $K_c$ is $9 \times 10^{-4}$. If equivalent amounts of $N_2$ and $O_2$ are used,what is the concentration of $NO$ at equilibrium (in terms of $a$) (in $, a$)?

Which of the following statements is/are wrong?
$(a)$ At equilibrium,concentrations of reactants and products become constant because the reaction stops.
$(b)$ Addition of catalyst speeds up the forward reaction more than the backward reaction.
$(c)$ Equilibrium constant of an exothermic reaction decreases with increase of temperature.
$(d)$ $K_p$ is always greater than $K_c$.

For the esterification reaction $CH_3COOH_{(l)} + C_2H_5OH_{(l)} \rightleftharpoons CH_3COOC_2H_{5(l)} + H_2O_{(l)}$,the equilibrium constant $K_c$ is $4$. If $4 \ mol$ of each acid and alcohol are taken initially,what will be the concentration of the acid at equilibrium?